Kinzinger is a member of the House Energy and Commerce Committee, which will hear from Sebelius next Wednesday.

He noted that Sebelius and other administration officials repeatedly told Congress that the exchanges would function as expected: "So one of two things either happened. Either they were dishonest to the committee and they had a whole lot of quote, 'glitches,' which seem to be more than glitches, or else they just didn't know. If they just didn't know this thing was going to be rolled out well, then that's incompetence. We have a lot of questions that need to be answered."

Kingzinger indicated that he'll listen to what Sebelius tells the committee before calling for her resignation. "It will be interesting what she has to say. But, ultimately, if this continues, yeah, I don't think there is any doubt that she needs to be replaced and move on."

He also mentioned that the huge amount of taxpayer money already spent on Obamacare won't be enough:

"Keep in mind, this isn't just a website. This cost hundreds of millions of taxpayer dollars to build something that isn't working. Now they are having to pull out all the stops and bring in all these experts, which they probably should have done at the very beginning."

Kinzinger said he also has doubts about how well the income verification process will work. He noted that an income verification provision was inserted into the stopgap spending bill, which Congress finally passed, ending the partial government shutdown.

The provision says people who apply for subsidies on the health insurance exchanges cannot self-report their income, but must have it verified by the IRS.

"Keep in mind, the administration -- one of the very small concessions that we actually got out of this continuing resolution deal was the income verification piece. Keep in mind, up until that happened, the administration said, you know what, we're just going to take your word for it for a year. So somebody can make $200,000 a year and say, you know what, I make at a level that I should get subsidy, and they'd just be taken at their word. So we actually got that done. But I don't have a whole lot of faith that the administration is going to follow through on enforcing that.

"And you see that 100 times. We pass bills out of Congress and the administration takes them and, in the execution of those bills, comes up with something totally different than the sense of Congress. You see overreach from the EPA. We'll see it in the HHS and all over from this administration. We have to be on top of this."